Sprinkle the turkey breast liberally with salt and pepper. Rub with the brown sugar and thyme. Wrap in foil and roast until the center registers 160 degrees F, 4 to 5 hours depending on the size of your turkey. Let cool completely before opening and slicing thinly across the grain. Refrigerate until ready to use.
For the turkey confit: Preheat the oven to 200 degrees F.
Warm the duck fat in a pan large enough to hold the legs and thighs. Rub the legs and thighs with salt and place in the pan, making sure they are completely submerged in the duck fat. Add a sachet of the thyme and the bay leaves to the fat. Cover with foil and cook until the meat is tender and pulls away effortlessly with a fork, 6 to 8 hours. Let cool, and then refrigerate in the fat overnight.
The following day, gently warm the confit enough to remove the turkey. Shred the meat into pieces and toss with a little bit of the fat; reserve about 2 tablespoons of the fat for rewarming the confit later. Press the confit into a baking dish or small baking tray. You want to press the confit into a single layer about 1/2 inch in height. Lay plastic wrap over the tray directly touching the confit. Place another tray on top and add a few cans or weights to press the confit; refrigerate overnight.
For the club sandwich: Lightly toast the bread. Unwrap the confit and cut a square of it about the same size as your bread. On a medium flame, heat the 2 tablespoons reserved duck fat in a nonstick pan. Place the square of confit in the pan and fry until brown and crisp on both sides.
Spread the mayo evenly over the bread slices, place the confit on one slice and top with another piece of bread. Next add the bacon, sliced tomato, turkey breast and lettuce. Top with the last piece of bread.